Shooting Method Calculator

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Example

Created on 2024-06-20Asked by Penelope Hill (Solvelet student)

Solve the boundary value problem

y'' = -y

y(0) = 0

y(\pi) = 0

using the shooting method.

Solution

To solve the boundary value problem

y'' = -y

y(0) = 0

y(\pi) = 0

using the shooting method: 1. **Define the initial value problems:** - First guess:

y(0) = 0

y'(0) = 1

. - Second guess:

y(0) = 0

y'(0) = -1

. 2. **Solve the initial value problems:** - First guess solution:

y = \sin(x)

. - Second guess solution:

y = -\sin(x)

. 3. **Apply boundary conditions:** - First guess at

x = \pi

y(\pi) = \sin(\pi) = 0

. - Second guess at

x = \pi

y(\pi) = -\sin(\pi) = 0

. 4. **Result:** Both solutions satisfy the boundary conditions, so

y = \sin(x)

and

y = -\sin(x)

are valid solutions. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Michael Miller on Solvelet

1. Use the shooting method to solve the boundary value problem

y'' + y = 0

y(0) = 0

y(\pi/2) = 1

.2. Apply the shooting method to solve the two-point boundary value problem

y'' + y = 0

y(0) = 0

y(1) = 1

DefinitionShooting is a numericalthat uses a differential boundary type. The central finite difference is applied to a boundary value problem to convert it into an initial problem. Example: To solve y′′+y=0 using the shooting method, where y(0)=1 and y(1)=0, the initial slope needs to be adjusted until y at x=1 is 0.

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